Prince Charles is facing a Westminster campaign to strip him and his estate of special privileges including tax exemptions, a power of veto over new laws and immunity from legislation covering everything from squatting to planning.

A radical bill is to be put before the House of Lords proposing to remove special treatment of the prince and the Duchy of Cornwall, his inherited £800m estate that provides him with a £19m a year private income.

The move, by the old-Etonian Labour peer Lord Berkeley, also exposes little-known exemptions from laws enforced on everyone else by at least eight acts of parliament.

In his capacity as the Duke of Cornwall, the prince cannot be prosecuted for breaches of planning laws such as building without permission or breaking the terms of planning consents, which would normally attract fines of up to £50,000. The prince's estate also enjoys an exemption from people registering land under squatters' rights or other forms of "adverse possession" until they have occupied it for 60 years, compared with 10 years for other landowners. Neither is it obliged to allow Duchy leaseholders to buy their freeholds.

"It is time for parliament to consider the increasingly urgent matter of the Prince of Wales's status and to modernise this medieval situation," Berkeley said. "The government and duchy both say the duchy is in the private sector yet it pays voluntary tax, gets free advice from government lawyers and has exemptions from legislation that applies to other private sector bodies."

Berkeley's bill would strip the prince of his power of veto over new legislation that might affect his private interests. Since 2005, ministers from at least six departments have sought his consent to draft bills on everything from road safety to gambling and the London Olympics. It has been described by constitutional lawyers as a royal "nuclear deterrent" over public policy.

Berkeley also wants parliament to remove the prince's right to claim legacies from ordinary people who die intestate in Cornwall. This right to bona vacantia provided more than £450,000 in 2012 and latest accounts show he is sitting on £3.3m in cash from many years of collecting Cornish legacies.

A spokeswoman for the prince said: "We do not comment on parliamentary procedure." His representatives have previously argued that bona vacantia money is used for charitable donations.

There is a growing move to change the terms of the prince's special constitutional status. Earlier this month, an appeal court ruled that the attorney general had been wrong to block the publication of his letters to government ministers. Last week, the Commons political and constitutional reform committee demanded changes to the "arcane" way he and the Queen consent to bills, saying it "fuels speculation the monarchy has an undue influence on the legislative process".

Berkeley's bill is unlikely ever to become law, but it is intended to add to the debate about some of the more controversial aspects of the prince's status. It proposes that he should pay income tax on his multimillion pound earnings in the normal way, rather than under the current voluntary arrangement, and that his estate should pay capital gains tax, which it currently does not do. Last year, Austin Mitchell MP, a member of the Commons public accounts committee, accused the prince's private secretary, William Nye, of "dodging around for tax purposes". The estate strongly denies any kind of tax avoidance. It asserts that it is "not a separate legal entity for tax purposes", allowing the prince to use its gross profits to fund his private and official spending. In the past five years he has received more than £86m from the arrangement. It also says that because he volunteers to pay income tax, payment of corporation tax would amount to double taxation.

Dr John Kirkhope, the legal scholar who has investigated the prince's special status, said the various arrangements were "profoundly offensive" and should be ended.

"What other private estate enjoys crown immunity so that it is not liable to capital gains tax?" he asked. "How many private estates have the right to give consent to legislation which has an effect on its operations?"

The exemptions from legislation enjoyed by the Duchy of Cornwall upended the fundamental legal principle of equality before the law and were outrageous, he said.